# A Matrix Product State Model for Simultaneous Classification and Generation

arXiv: https://arxiv.org/abs/2406.17441 · HTML: https://mlsanity.com/paper/2406.17441/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 56 references that are in the map.
- First posted on arXiv 25 Jun 2024.

## Builds on (most cited first, 17 of 17)

- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Unsupervised Generative Modeling Using Matrix Product States](https://mlsanity.com/paper/1709.01662/) (2017)
- [Algorithms for Solving High Dimensional PDEs: From Nonlinear Monte Carlo to Machine Learning](https://mlsanity.com/paper/2008.13333/) (2020)
- [Tree Tensor Networks for Generative Modeling](https://mlsanity.com/paper/1901.02217/) (2019)
- [Expressive power of tensor-network factorizations for probabilistic modeling, with applications from hidden Markov models to quantum machine learning](https://mlsanity.com/paper/1907.03741/) (2019)
- [Supervised Learning with Quantum-Inspired Tensor Networks](https://mlsanity.com/paper/1605.05775/) (2016)
- [Supervised Learning with Projected Entangled Pair States](https://mlsanity.com/paper/2009.09932/) (2020)
- [TensorNetwork for Machine Learning](https://mlsanity.com/paper/1906.06329/) (2019)
- [Grokking phase transitions in learning local rules with gradient descent](https://mlsanity.com/paper/2210.15435/) (2022)
- [Tensorized Embedding Layers for Efficient Model Compression](https://mlsanity.com/paper/1901.10787/) (2019)
- [Tensor networks for unsupervised machine learning](https://mlsanity.com/paper/2106.12974/) (2021)
- [Generative modeling with projected entangled-pair states](https://mlsanity.com/paper/2202.08177/) (2022)
- [Canonical normalizing flows for manifold learning](https://mlsanity.com/paper/2310.12743/) (2023)
- [Privacy-preserving machine learning with tensor networks](https://mlsanity.com/paper/2202.12319/) (2022)
- [Matrix Product State for Higher-Order Tensor Compression and Classification](https://mlsanity.com/paper/1609.04541/) (2016)
- [Positive unlabeled learning with tensor networks](https://mlsanity.com/paper/2211.14085/) (2022)

## Built on by (most cited first, 6 of 6)

- [Tensorization of neural networks for improved privacy and interpretability](https://mlsanity.com/paper/2501.06300/) (2025)
- [Using matrix-product states for time-series machine learning](https://mlsanity.com/paper/2412.15826/) (2024)
- [Hyperbolic Optimization](https://mlsanity.com/paper/2509.25206/) (2025)
- [Private and interpretable clinical prediction with quantum-inspired tensor train models](https://mlsanity.com/paper/2602.06110/) (2026)
- [Quantum-inspired tensor networks in machine learning models](https://mlsanity.com/paper/2604.14287/) (2026)
- [Gaussian Universality and Its Breakdown in Tensor-Network Machine Learning](https://mlsanity.com/paper/2610.06080/) (2026)

## Abstract (arXiv)

Quantum machine learning (QML) is a rapidly expanding field that merges the principles of quantum computing with the techniques of machine learning. One of the powerful mathematical frameworks in this domain is tensor networks. These networks are used to approximate high-order tensors by contracting tensors with lower ranks. Initially developed for simulating quantum systems, tensor networks have become integral to quantum computing and, by extension, to QML. Drawing inspiration from these quantum methods, specifically the Matrix Product States (MPS), we apply them in a classical machine learning setting. Their ability to efficiently represent and manipulate complex, high-dimensional data makes them effective in a supervised learning framework. Here, we present an MPS model, in which the MPS functions as both a classifier and a generator. The dual functionality of this novel MPS model permits a strategy that enhances the traditional training of supervised MPS models. This framework is inspired by generative adversarial networks and is geared towards generating more realistic samples by reducing outliers. In addition, our contributions offer insights into the mechanics of tensor network methods for generation tasks. Specifically, we discuss alternative embedding functions and a new sampling method from non-normalized MPSs.